A316829 Image of 0 under repeated application of the morphism 0 -> 0,1,0, 1 -> 1,1,1.

0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0

Comments

A word that is pure uniform morphic and recurrent, but not primitive morphic.

Links

Antti Karttunen, Table of n, a(n) for n = 0..19682

Jean-Paul Allouche, Julien Cassaigne, Jeffrey Shallit, Luca Q. Zamboni, A Taxonomy of Morphic Sequences, arXiv preprint arXiv:1711.10807 [cs.FL], Nov 29 2017.

Index entries for characteristic functions

Index entries for sequences that are fixed points of mappings

Formula

a(n) = 1 - A088917(n) = A105220(n) - 1. - Antti Karttunen, Sep 27 2019

Mathematica

SubstitutionSystem[{0 -> {0, 1, 0}, 1 -> {1, 1, 1}}, {0}, 5] // Last (* Jean-François Alcover, Aug 05 2018 *)

Prog

(PARI) A316829(n) = { while(n, if(n%3==1, return(1), n\=3)); (0); }; \\ Antti Karttunen, Sep 27 2019

Crossrefs

Sequences mentioned in the Allouche et al. "Taxonomy" paper, listed by example number: 1: A003849, 2: A010060, 3: A010056, 4: A020985 and A020987, 5: A191818, 6: A316340 and A273129, 18: A316341, 19: A030302, 20: A063438, 21: A316342, 22: A316343, 23: A003849 minus its first term, 24: A316344, 25: A316345 and A316824, 26: A020985 and A020987, 27: A316825, 28: A159689, 29: A049320, 30: A003849, 31: A316826, 32: A316827, 33: A316828, 34: A316344, 35: A043529, 36: A316829, 37: A010060.

Cf. A088917, A105220.

Characteristic function of A081606.

Sequence in context: A276950 A285351 A284893 * A277674 A309754 A112690

Adjacent sequences: A316826 A316827 A316828 * A316830 A316831 A316832

Keyword

nonn

Author

N. J. A. Sloane, Jul 15 2018

Status

approved